695 research outputs found
Swing Dynamics as Primal-Dual Algorithm for Optimal Load Control
Frequency regulation and generation-load balancing are key issues in power transmission networks. Complementary to generation control, loads provide flexible and fast responsive sources for frequency regulation, and local frequency measurement capability of loads offers the opportunity of decentralized control. In this paper, we propose an optimal load control problem, which balances the load reduction (or increase) with the generation shortfall (or surplus), resynchronizes the bus frequencies, and minimizes a measure of aggregate disutility of participation in such a load control. We find that, a frequency-based load control coupled with the dynamics of swing equations and branch power flows serve as a distributed primal-dual algorithm to solve the optimal load control problem and its dual. Simulation shows that the proposed mechanism can restore frequency, balance load with generation and achieve the optimum of the load control problem within several seconds after a disturbance in generation. Through simulation, we also compare the performance of optimal load control with automatic generation control (AGC), and discuss the effect of their incorporation
Design and Stability of Load-Side Primary Frequency Control in Power Systems
We present a systematic method to design ubiquitous continuous fast-acting
distributed load control for primary frequency regulation in power networks, by
formulating an optimal load control (OLC) problem where the objective is to
minimize the aggregate cost of tracking an operating point subject to power
balance over the network. We prove that the swing dynamics and the branch power
flows, coupled with frequency-based load control, serve as a distributed
primal-dual algorithm to solve OLC. We establish the global asymptotic
stability of a multimachine network under such type of load-side primary
frequency control. These results imply that the local frequency deviations at
each bus convey exactly the right information about the global power imbalance
for the loads to make individual decisions that turn out to be globally
optimal. Simulations confirm that the proposed algorithm can rebalance power
and resynchronize bus frequencies after a disturbance with significantly
improved transient performance.Comment: 14 pages, 13 figures. To appear in IEEE Transactions on Automatic
Contro
Optimal load-side control for frequency regulation in smart grids
Frequency control rebalances supply and demand while maintaining the network
state within operational margins. It is implemented using fast ramping reserves
that are expensive and wasteful, and which are expected to grow with the
increasing penetration of renewables. The most promising solution to this
problem is the use of demand response, i.e. load participation in frequency
control. Yet it is still unclear how to efficiently integrate load
participation without introducing instabilities and violating operational
constraints.
In this paper we present a comprehensive load-side frequency control
mechanism that can maintain the grid within operational constraints. In
particular, our controllers can rebalance supply and demand after disturbances,
restore the frequency to its nominal value and preserve inter-area power flows.
Furthermore, our controllers are distributed (unlike the currently implemented
frequency control), can allocate load updates optimally, and can maintain line
flows within thermal limits. We prove that such a distributed load-side control
is globally asymptotically stable and robust to unknown load parameters. We
illustrate its effectiveness through simulations.Comment: Under revisio
Less is More: Real-time Failure Localization in Power Systems
Cascading failures in power systems exhibit non-local propagation patterns
which make the analysis and mitigation of failures difficult. In this work, we
propose a distributed control framework inspired by the recently proposed
concepts of unified controller and network tree-partition that offers strong
guarantees in both the mitigation and localization of cascading failures in
power systems. In this framework, the transmission network is partitioned into
several control areas which are connected in a tree structure, and the unified
controller is adopted by generators or controllable loads for fast timescale
disturbance response. After an initial failure, the proposed strategy always
prevents successive failures from happening, and regulates the system to the
desired steady state where the impact of initial failures are localized as much
as possible. For extreme failures that cannot be localized, the proposed
framework has a configurable design, that progressively involves and
coordinates more control areas for failure mitigation and, as a last resort,
imposes minimal load shedding. We compare the proposed control framework with
Automatic Generation Control (AGC) on the IEEE 118-bus test system. Simulation
results show that our novel framework greatly improves the system robustness in
terms of the N-1 security standard, and localizes the impact of initial
failures in majority of the load profiles that are examined. Moreover, the
proposed framework incurs significantly less load loss, if any, compared to
AGC, in all of our case studies
Distributed Frequency Control with Operational Constraints, Part I: Per-Node Power Balance
This paper addresses the distributed optimal frequency control of multi-area power system with operational constraints, including the regulation capacity of individual control area and the power limits on tie-lines. Both generators and controllable loads are utilized to recover nominal frequencies while minimizing regulation cost. We study two control modes: 1) the per-node balance mode and 2) the network balance mode. In Part I of this paper, we only consider the per-node balance case, where we derive a completely decentralized strategy without the need for communication between control areas. It can adapt to unknown load disturbance. The tie-line powers are restored after load disturbance, while the regulation capacity constraints are satisfied both at equilibrium and during transient. We show that the closed-loop systems with the proposed control strategies carry out primal-dual updates for solving the associated centralized frequency optimization problems. We further prove the closed-loop systems are asymptotically stable and converge to the unique optimal solution of the centralized frequency optimization problems and their duals. Finally, we present simulation results to demonstrate the effectiveness of our design. In Part II of this paper, we address the network power balance case, where transmission congestions are managed continuously
Online Optimization as a Feedback Controller: Stability and Tracking
This paper develops and analyzes feedback-based online optimization methods
to regulate the output of a linear time-invariant (LTI) dynamical system to the
optimal solution of a time-varying convex optimization problem. The design of
the algorithm is based on continuous-time primal-dual dynamics, properly
modified to incorporate feedback from the LTI dynamical system, applied to a
proximal augmented Lagrangian function. The resultant closed-loop algorithm
tracks the solution of the time-varying optimization problem without requiring
knowledge of (time-varying) disturbances in the dynamical system. The analysis
leverages integral quadratic constraints to provide linear matrix inequality
(LMI) conditions that guarantee global exponential stability and bounded
tracking error. Analytical results show that, under a sufficient time-scale
separation between the dynamics of the LTI dynamical system and the algorithm,
the LMI conditions can be always satisfied. The paper further proposes a
modified algorithm that can track an approximate solution trajectory of the
constrained optimization problem under less restrictive assumptions. As an
illustrative example, the proposed algorithms are showcased for power
transmission systems, to compress the time scales between secondary and
tertiary control, and allow to simultaneously power re-balancing and tracking
of DC optimal power flow points
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